David Cameron's statement that this will be the greenest government ever will be treated with weary scepticism by those brought up on a diet of grand Blairite claims. There are, however, grounds for cautious optimism. The unusual nature of the politics of the coalition government provides the prime minister with a strong political interest in delivering some big wins on the environmental agenda.

Along with civil liberties and electoral reform, the environment is central to the Liberal Democrats' sense of political identity. As one Lib Dem insider recently told me: "If we can't make progress on green issues it wouldn't have been worth joining the coalition." It's an agenda that Nick Clegg will hope to use to bind the Lib Dem base into the coalition over coming months.

Paradoxically, it was an area where there was relatively little difference between the Conservative and Lib Dem manifestos. This is in large part due to David Cameron's leadership, making the environment a key part of his project to modernise the Conservative party.

Interestingly, public deficit reduction will force the coalition to drive the green agenda using policy levers that will feel distinctly un-Conservative to many of the party's traditional supporters. But this is familiar territory to centre-right parties in Europe.

The first is taxation. I predict that we'll see the party of low taxation overseeing a growth in green taxation. While it will upset the right of the Conservative party, the logic for George Osborne is compelling. He has already made it clear that 20% of the structural deficit will have to be corrected using increased tax revenues (with the rest from cuts in public spending). New tax revenues can either come from taxation of income, as Labour proposed in their plan to increase National Insurance contributions, or from taxing resources, such as the reform of air passenger duty or the climate change levy. One taxes jobs - the thing we most value in the economic recovery - while the other taxes pollution and decreases damage to our environment. So in tomorrow's budget the least painful route to generating new tax revenue lies in following through on the Coalition agreement to increase green taxation.

The second trend, which also challenges Conservative party orthodoxy, is an increase in green regulation. It will be focused on stimulating cost reduction and business innovation in specific sectors of our economy, and should reduce public subsidy over time. It will be the state using its legal powers to drive change in private sector investment, and will complement Cameron's commitment to using "nudge" type policies to drive individual behaviour. A step too far for the Conservatives? Not according to the coalition agreement where 19 of the 23 green policies will be delivered by this route. Feed-in tariffs, an emissions performance standard for coal power stations and the establishment of a smart grid all require smart regulation and have the obvious attraction of imposing no direct cost on government.

Last, there is a real possibility that we'll see the Cameron-Clegg government apply its reforming zeal to the perennial problem of the European budget, still largely focused on supporting agriculture at the expense of both clean technology and nature conservation. The Conservative leadership is surprisingly comfortable dealing with Europe on environmental issues. In a recent speech to Green Alliance, William Hague made it clear that it is a priority to "fundamentally reform the EU budget … to redirect resources to climate change and energy security".

So where do the dangers lurk for the green agenda? The biggest come from opponents of the coalition. Because the environmental agenda is providing glue to hold the new government together, it's also a place where critics will attack. Christopher Brooker of the Daily Telegraph has been railing against the "warmists" who will "close down our economy" and has already identified the environment agenda as the "Achilles heel" of the new administration.

This points to two things the government has to do if its green ambitions are to be delivered. The first is that Osborne will have to protect consumers from unsustainable rises in energy prices. Some of this can be done by encouraging more competition in the market, but the real source of cost reduction will come from technology breakthroughs. For this to happen we need government to increase rather than decrease its limited expenditure on low-arbon research and development. This will be a tough call in the current fiscal environment.

Second, it is essential that David Cameron and his most senior Conservative colleagues lead from the front on climate change as they did in opposition. The Liberal Democrats in Cabinet cannot do it alone. The prime minister, the chancellor and the foreign secretary will have to invest political capital if they are to protect their Lib Dem flank from those on the right and the left who will try to split the two coalition parties on this agenda.

Being the greenest government ever may not seem like a big achievement given the patchy performance of previous administrations, but for the coalition it will be a major test. If they can't achieve rapid progress on green issues their legitimacy will fade in the eyes of Liberal Democrats supporters and those who voted Conservative in the belief that it was a reformed, modern party. If they do manage to deliver on their commitments it will be a badge of honour for the new politics of Cameron and Clegg.

• Matthew Spencer is the director of the Green Alliance, an environmental thinktank